You want to confirm that the dynamic linker's cache already knows about libssl.so.3, without running or even having a program that uses it. Which command lists the cache contents?

LPIC-1 Exam 101-500, objective 102. Linux installation and package management easy

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The options

Correct ldconfig -p

Correct. -p prints the libraries currently listed in /etc/ld.so.cache together with the paths they resolve to, so it can be piped to grep.

Not correct ldd libssl.so.3

Wrong for this purpose. ldd reports what a given file itself depends on; it needs a real path to a binary or library and says nothing about the cache.

Not correct ldconfig -v

Wrong. -v rebuilds the cache while printing what it scans, so it modifies the system rather than only reporting on it.

Not correct cat /etc/ld.so.conf

Wrong. That file lists the directories to be searched, not the libraries found in them, and on most distributions it does little more than include /etc/ld.so.conf.d/*.conf.

Why

ldconfig has two modes: run with no options it rescans the configured directories and rewrites /etc/ld.so.cache, and with -p it only prints what the cache already contains. The distinction to carry is configuration versus cache: /etc/ld.so.conf and its .conf drop-ins say where to look, the cache is the compiled result, and ld.so reads only the cache at program start-up.

Where this comes from

Cited
manual page ldconfig(8)

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